Measurement of Strong-Phase Difference Between \(D^{0}\) and  \(\bar{D^{0}}\rightarrow K^{0}_\textrm{S,L}K^{+}K^{-}\) Decay at BESIII

We measure the strong-phase difference between \(D^{0}\) and \(\bar{D^{0}}\rightarrow K^{0}_\textrm{S,L}K^{+}K^{-}\) using a data sample corresponding to an integrated luminosity of 2.92 fb \(^{-1}\) collected in \(e^{+}e^{-}\) collisions at a centre-of-mass energy corresponding to the mass of the \(\psi (3770)\) . The \(D^{0}-\bar{D^{0}}\) meson pairs produced are in a quantum-correlated state, their subsequent decays are recorded by the BESIII 4 \(\pi \) magnetic spectrometer. The measured values of strong-phase difference is most precise to this date. The measured value of the strong-phase difference is an essential input to determining the value of Cabbibo-Kobayashi-Maskawa (CKM) angle \(\gamma /\phi _{3}\) through the decay \(B^{-} \rightarrow \tilde{D}K^{-}\) , where D can be \(D^{0}\) or \(\bar{D^{0}}\) decaying to \(K^{0}_\textrm{S,L}K^{+}K^{-}\) .